0
TECHNICAL PAPERS

Plastic Yielding as a Phase Transition

[+] Author and Article Information
M. Ortiz

Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125

J. Appl. Mech 66(2), 289-298 (Oct 25, 1999) (9 pages) doi:10.1115/1.2791048 History: Received August 14, 1998; Revised November 20, 1998

Abstract

A statistical mechanical theory of forest hardening is developed in which yielding arises as a phase transition. For simplicity, we consider the case of a single dislocation loop moving on a slip plane through randomly distributed forest dislocations, which we treat as point obstacles. The occurrence of slip at the sites occupied by these obstacles is assumed to require the expenditure of a certain amount of work commensurate with the strength of the obstacle. The case of obstacles of infinite strength is treated in detail. We show that the behavior of the dislocation loop as it sweeps the slip plane under the action of a resolved shear stress is identical to that of a lattice gas, or, equivalently, to that of the two-dimensional spin-1/2 Ising model. In particular, there exists a critical temperature Tc below which the system exhibits a yield point, i.e., the slip strain increases sharply when the applied resolved shear stress attains a critical value. Above the critical temperature the yield point disappears and the slip strain depends continuously on the applied stress. The critical exponents, which describe the behavior of the system near the critical temperature, coincide with those of the two-dimensional spin-1/2 Ising model.

COPYRIGHT © 1999 by The American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

AbeyaratneRKnowlesJK1988On the dissipative response due to discontinuous strains in bars of unstable elastic materialInternational Journal of Solids and Structures66210211044 [CrossRef]
BaskesMIHoaglandRGTsujiT1997An atomistic study of the strength of an extended dislocation barrier
BaxterRJExactly Solved Models in Statistical Mechanics Academic Press London
BinderK1986Monte Carlo Methods in Statistical Physics2 Springer-Verlag New York
BinderK1987Applications of the Monte Carlo Method in Statistical Physics2 Springer-Verlag New York
BinneyJJDowrickNJFisherAJNewmanMEJ1992The Modern Theory of Critical Phenomena Clarendon Press Oxford
ChaikinPMLubenskyTC1995Principles of condensed matter physics Cambridge University Press Cambridge, UK
ChrzanDCMillsMJ1993Collective behavior and superdislocation motion in l12 alloysMaterials Science and Engineering A6628292 [CrossRef]
ChrzanDCMillsMJ1994Criticality in the plastic deformation of l12 intermetallic compoundsPhysical Review B6623042 [CrossRef]
Cuitin˜oAM1996Effect of temperature and stacking fault energy on the hardening of fcc crystalsMaterials Science and Engineering662104116
Cuitin˜oAMOrtizM1992Computational Modelling of Single CrystalsModelling and Simulation in Materials Science and Engineering662255263
Cuitin˜oAMOrtizM1993Constitutive Modeling of L12 Intermetallic CrystalsMaterials Science and Engineering662111123
EricksenJL1975Equilibrium of barsJournal of Elasticity662191201 [CrossRef]
FeynmanRP1972Statistical Mechanics Addison-Wesley Reading, MA
ForemanAJ1995Dislocation energies in anisotropic crystalsActa Metallurgica662322330
ForemanAJEMakinMJ1966Dislocation Movement through Random Arrays of ObstaclesPhilosophical Magazine662911 [CrossRef]
ForemanAJEMakinMJ1967Dislocation movement through random arrays of obstaclesCanadian J. Phys662273
GrosskreutzJCMughrabiH1975Description of the work-hardened structure at low temperature in cyclic deformationConstitutive Equations in PlasticityArgonAS M.I.T. Press Cambridge, MA251326
GuggenheimEA1945The Principle of Corresponding StatesJournal of Chemical Physics662253261 [CrossRef]
HansenNKuhlmann-WilsdorffD1986Low Energy Dislocation Structures due to Unidirectional Deformation at Low TemperaturesMaterials Science and Engineering662141161 [CrossRef]
HirthJPLotheJ1968Theory of Dislocations McGraw-Hill New York
JamesRD1979Co-exitent phases in the one-dimensional theory of elastic barsArchive for Rational Mechanics and Analysis66299140
KocksUF1964Latent hardening and secondary slip in aluminum and silverTransactions of the Metallurgical Society of the AIME6621160
KocksUFFranciosiPKawaiM1991A forest model of latent hardening and its applications to polycrystal deformationTextures and Microstructares66211031114 [CrossRef]
KooninSEMeredithDC1990Computational Physics Addison-Wesley Reading, MA
KosterlitzJMThoulessDJ1972Long Range Order and Metastability in Two Dimensional Solids and SuperfluidsJournal of Physics C662L124L126
KosterlitzJMThoulessDJ1973Ordering, Metastability and Phase Transitions in Two-Dimensional SystemsJournal of Physics C66211811203 [CrossRef]
KovacsI1967The Mechanism of the Work-Harderning in F.C.C. MetalsActa Metallurgica17311736
Kova'csIZsoldosL1973Dislocation and plastic deformation Pergamon Press Oxford, UK
Kuhlmann-WilsdorfD1979Dislocation behavior in fatigue. IV. Quantitative interpretation of friction stress and back stress derived from hysteresis loopsMaterials Science and Engineering662231245 [CrossRef]
Kuhlmann-WilsdorfD1989Theory of plastic deformation: properties of low energy dislocation structuresMaterials Science and Engineering6621 [CrossRef]
MughrabiH1975Description of the Dislocation Structure after Unidirectional Deformation at Low TemperaturesConstitutive Equations in PlasticityArgonAS M.I.T. Press Cambridge, MA199250
NabarroFRN1967Theory of crystal dislocations Oxford University Press Oxford, UK
NelsonDRHalperinBI1979Dislocation-Mediated Melting in Two DimensionsPhysical Review B66224572484 [CrossRef]
OrtizMPopovEP1962A Statistical Theory of Polycrystalline PlasticityProceedings of the Royal Society of London662439458
OrtizMRepettoEA1998Nonconvex energy minimization and dislocation structures in ductile single crystalsJournal of the Mechanics and Physics of Solidsin press
PhillipsRShenoyV1998manuscript in preparation
StanleyHE1971Introduction to Phase Transitions and Critical Phenomena Oxford University Press Oxford, UK
YeomansJM1992Statistical Mechanics of Phase Transitions Clarendon Press Oxford, UK
YoungAP1979Melting and the Vector Coulomb Gas in two DirectionsPhysical Review B66218551866 [CrossRef]

Figures

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In